Consider the expression [tex](8.1\cdot 10^{-4})^2.[/tex]
Use main properties for powers:
1. [tex](a\cdot b)^m=a^m\cdot b^m;[/tex]
2. [tex](a^m)^n=a^{m\cdot n};[/tex]
3. [tex]a^m\cdot a^n=a^{m+n}.[/tex]
Then
[tex](8.1\cdot 10^{-4})^2=8.1^2\cdot (10^{-4})^2=65.61\cdot 10^{-4\cdot 2}=65.61\cdot 10^{-8}=6,561\cdot 10^{-2}\cdot 10^{-8}=6,561\cdot 10^{-10}.[/tex]
The result in scientific notation is [tex]6,561\cdot 10^{-10}.[/tex]
The result as a decimal is [tex]0.0000006561.[/tex]
